NK groups

Summary

The groups $NK_n(R)$ measure how far the K-theory of a polynomial ring $R[t]$ differs from the K-theory of $R$. The group $K_n(R[t])$ splits as $K_n(R) \oplus NK_n(R)$. They vanish when $R$ is regular Noetherian, which is the homotopy invariance of K-theory. They appear twice in the fundamental theorem for Laurent polynomial rings, and they are often large when they are not zero.